To evaluate the expression \(-6 \frac{1}{10} - 2 \frac{1}{5} + (-9.3) + 2.2\), we will first convert all the mixed numbers to improper fractions and decimal form, and then perform the calculations step by step.
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Convert the mixed numbers to improper fractions:
- \(-6 \frac{1}{10} = -\frac{61}{10}\)
- \(-2 \frac{1}{5} = -\frac{11}{5} = -\frac{22}{10}\) (converting to a common denominator of 10)
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Convert the decimals to fractions:
- \(-9.3 = -\frac{93}{10}\)
- \(2.2 = \frac{22}{10}\)
Now, our expression can be rewritten as: \[ -\frac{61}{10} - \frac{22}{10} - \frac{93}{10} + \frac{22}{10} \]
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Combine all the fractions: \[ -\frac{61 + 22 + 93 - 22}{10} = -\frac{61 + 93}{10} = -\frac{154}{10} \]
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Simplify \(-\frac{154}{10}\): \[ -\frac{154 \div 2}{10 \div 2} = -\frac{77}{5} \]
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Convert \(-\frac{77}{5}\) to a mixed number:
- Divide \(77\) by \(5\): \(77 \div 5 = 15\) remainder \(2\).
- Hence, \(-\frac{77}{5} = -15 \frac{2}{5}\).
Thus, the final answer is: \[ \boxed{-15 \frac{2}{5}} \]